Mapping of number onto space is fundamental to mathematics and measurement. Previous research suggests that while typical adults with mathematical schooling map numbers veridically onto a linear scale, pre-school children and adults without formal mathematics training, as well as individuals with dyscalculia, show strong compressive, logarithmic-like non-linearities when mapping both symbolic and non-symbolic numbers onto the numberline. Here we show that the use of the linear scale is dependent on attentional resources. We asked typical adults to position clouds of dots on a numberline of various lengths. In agreement with previous research, they did so veridically under normal conditions, but when asked to perform a concurrent attentionally-demanding conjunction task, the mapping followed a compressive, non-linear function. We model the non-linearity both by the commonly assumed logarithmic transform, and also with a Bayesian model of central tendency. These results suggest that veridical representation numerosity requires attentional mechanisms.

For visual localization to remain accurate across changes of gaze, a signal representing the position of the eye in the orbita is needed to code spatial locations in a reference frame that is independent of retinal displacements. Here we report evidence that the localization of visual objects in space is coded in an extraretinal reference frame. In human subjects, we used outward saccadic adaptation, which can be induced artificially by a systematic displacement of the saccade target. This form of oculomotor plasticity is accompanied by changes in spatial perception, thus highlighting the relevance of saccade metrics for visual localization. We tested the reference frame of outward adaptation for reactive and scanning saccades and visual localization. For scanning saccades, adaptation magnitude was drastically reduced at positions distant from the adapted eye position. Changes in visual localization showed a very similar modulation of eye position. These results suggest that scanning saccade adaptation is encoded in a nonretinotopic reference frame. Eye position effects for reactive saccade adaptation were smaller, and the induced mislocalization did not vary significantly between eye positions. The different modulation of reactive and scanning saccade adaptation supports the idea that oculomotor plasticity can occur at multiple sites in the brain. The findings are also consistent with previous evidence for a stronger influence of scanning saccade adaptation on the visual localization of objects in space.

Saccadic adaptation is a powerful experimental paradigm to probe the mechanisms of eye movement control and spatial vision, in which saccadic amplitudes change in response to false visual feedback. The adaptation occurs primarily in the motor system, but there is also evidence for visual adaptation, depending on the size and the permanence of the postsaccadic error. Here we confirm that adaptation has a strong visual component and show that the visual component of the adaptation is spatially selective in external, not retinal coordinates. Subjects performed a memory-guided, double-saccade, outward-adaptation task designed to maximize visual adaptation and to dissociate the visual and motor corrections. When the memorized saccadic target was in the same position (in external space) as that used in the adaptation training, saccade targeting was strongly influenced by adaptation (even if not matched in retinal or cranial position), but when in the same retinal or cranial but different external spatial position, targeting was unaffected by adaptation, demonstrating unequivocal spatiotopic selectivity. These results point to the existence of a spatiotopic neural representation for eye movement control that adapts in response to saccade error signals.

Adaptive shortening of a saccade influences the metrics of other saccades withina spatial window around the adapted target. Within this adaptation field visualstimuli presented before an adapted saccade are mislocalized in proportion to thechange of the saccade metric. We investigated the saccadic adaptation field andassociated localization changes for saccade lengthening, or outward adaptation. Wemeasured the adaptation field for two different saccade adaptations (14 deg to 20deg and 20 deg to 26 deg) by testing transfer to 34 different target positions. Wemeasured localization judgements by asking subjects to localize a probe flashedbefore saccade onset. The amount of adaptation transfer differed for different targetlocations. It increased with increases of the horizontal component of the saccade andremained largely constant with deviation of the vertical component of the saccade.Mislocalization of probes inside the adaptation field was correlated with the amountof adaptation of saccades to the probe location. These findings are consistent withthe assumption that oculomotor space and perceptual space are linked to each other.

We demonstrate a strong sensory-motor coupling in visual localization in which experimental modification of the control of saccadic eye movements leads to an associated change in the perceived location of objects. Amplitudes of saccades to peripheral targets were altered by saccadic adaptation, induced by an artificial step of the saccade target during the eye movement, which leads the oculomotor system to recalibrate saccade parameters. Increasing saccade amplitudes induced concurrent shifts in perceived location of visual objects. The magnitude of perceptual shift depended on the size and persistence of errors between intended and actual saccade amplitudes. This tight agreement between the change of eye movement control and the change of localization shows that perceptual space is shaped by motor knowledge rather than simply constructed from visual input.

The gist of a visual scene is perceived in a fraction of a second but in change detection tasks subjects typically need several seconds to find the changing object in a visual scene. Here, we report influences of scene context on change detection performance. Scene context manipulations consisted of scene inversion, scene jumbling, where the images were cut into 24 pieces and randomly recombined, and scene configuration scrambling, where the arrangement of the objects in the scene was randomized. Reaction times, where significantly lower in images with normal scene context. We conclude that scene context structures scene perception.

When we look around and register the location of visual objects, our oculomotor system continuously prepares targets for saccadic eye movements. The preparation of saccade targets may be directly involved in the perception of object location because modification of saccade amplitude by saccade adaptation leads to a distortion of the visual localization of briefly flashed spatial probes. Here, we investigated effects of adaptation on the localization of continuously visible objects. We compared adaptation-induced mislocalization of probes that were present for 20 ms during the saccade preparation period and of probes that were present for >1 s before saccade initiation. We studied the mislocalization of these probes for two different saccade types, reactive saccades to a suddenly appearing target and scanning saccades in the self-paced viewing of a stationary scene. Adaptation of reactive saccades induced mislocalization of flashed probes. Adaptation of scanning saccades induced in addition also mislocalization of stationary objects. The mislocalization occurred in the absence of visual landmarks and must therefore originate from the change in saccade motor parameters. After adaptation of one type of saccade, the saccade amplitude change and the mislocalization transferred only weakly to the other saccade type. Mislocalization of flashed and stationary probes thus followed the selectivity of saccade adaptation. Since the generation and adaptation of reactive and scanning saccades are known to involve partially different brain mechanisms, our results suggest that visual localization of objects in space is linked to saccade targeting at multiple sites in the brain.